 "Solutions to the RH and and related mathematical research areasDisclaimer: with the exception of the last section D all papers of this page are without authorization from the ivory tower
for the latest updated version see http://www.fuchsbraun.com A. A Kummer function based Zeta function theory to prove the Riemann Hypothesis
http://www.riemannhypothesis.de
B. A new ground state energy model of the harmonic quantum oscillator
Abstract
We provide a new ground state energy model which ensures convergent quantum oscillator energy series. This enables the definition of a truly infinitesimal geometry based on a nonordered, still Archimedian field. The corresponding inner product with its induced norm defines the appropriate metric. The (Hilbert space) domains of related selfadjoint, positive definite operators to build appropriate eigenpair structures are built on Cartan´s differential forms. By this, H. Weyl´s "truly" infinitesimal (affine connexions, parallel displacements, differentiable manifolds based) geometry is replaced by a truly infinitesimal (rotation group based) geometry (corresponding to continuous manifolds, only):
May 2017 summary
A new H(1/2) Hilbert space based ground state energy model of the harmonic quantum oscillator
Relationships/opportunities to a related quantum gravity model
Further related/supporting papers
Braun K., "An alternative quantization of H=xp"
http://www.fuchsbraun.com/media/e9ed39ef818176fffff8031fffffff2.pdf
C. A global unique weak H(1/2) solution of the NavierStokes initial value problem
earlier published versions
D. PhD thesis
Besides the interior error estimates the paper proves the quasioptimal approximation behavior of the RitzGalerkin method in a Hilbert scale framework. The example 2 gives the model operator of the Symm (PseudoDifferential) integral operator. Other examples would be the CalderonZygmund (singular integral) operator or the Hilbert transform (singular integral) operator.
